Phase field equations with memory: The hyperbolic case

Horacio G. Rotstein, Simon Brandon, Amy Novick-Cohen, Alexander Nepomnyashchy

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


We present a phenomenological theory for phase transition dynamics with memory which yields a hyperbolic generalization of the classical phase field-model when the relaxation kernels are assumed to be exponential. Thereafter, we focus on the implications of our theory in the hyperbolic case, and we derive asymptotically an equation of motion in two dimensions for the interface between two different phases. This equation can be considered as a hyperbolic generalization of the classical flow by mean curvature equation, as well as a generalization of the Born-Infeld equation. We use a crystalline algorithm to study the motion of closed curves for our hyperbolic generalization of flow by mean curvature and present some numerical results which indicate that a certain type of two-dimensional damped oscillation may occur.

Original languageEnglish (US)
Pages (from-to)264-282
Number of pages19
JournalSIAM Journal on Applied Mathematics
Issue number1
StatePublished - 2001
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Applied Mathematics


  • Crystalline algorithms
  • Mean curvature flow
  • Memory effects
  • Phase field equations
  • Phase transitions


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